Advances in Robot Navigation Part 7 doc

If any robots exist within A Ti , ri selects the first neighbor rn1 and defines its position pn1.. 5.3 Unification function In order to enable multiple swarms in close proximity to merg

computes Oi at the time t By rotating Ti 90 degrees clockwise and counterclockwise, respectively, two vectors Ti,c and Ti,a are defined Within ri’s SB, an area of traveling direction

A Ti is defined as the area between Ti,cand Ti,aas illustrated in Fig 7-(b) Under ALGORITHM-2, ri checks whether there exists a neighbor in A Ti If any robots exist within A Ti , ri selects the first neighbor rn1 and defines its position pn1 Otherwise, ri spots a virtual point pv located some distance dv away from pi along A Ti , which gives pn1 After determining pn1, rn2 is selected and its position pn2 is defined

(a) traveling direction Ti (b) maintenance area A Ti Fig 7 Illustration of the maintenance function

5.2 Partition function

(a) favorite vector fj (b) partition area A fjmax Fig 8 Illustration of the partition function

When ri detects an obstacle that blocks its way to the destination, it is required to modify the direction toward the destination avoiding the obstacle In this work, ri determines its direction by using the relative degree of attraction of individual passageways sj, termed the favorite vector fj, whose magnitude is given:

f = w

where wj and dj denote the width of sj and the distance between the center of wj and pi, respectively Note that if ri can not exactly measure wj beyond its SB, wj may be shortened Now, sj can be represented by a set of favorite vectors fj1≤j≤m , and then ri selects the maximum magnitude of fj, denoted as fj max Similar to defining A Ti above, ri defines a maximum favorite area A fjmax based on the direction of fj max within its SB If neighbors are found in A fjmax , ri selects rn1 to define pn1 Otherwise, ri spots a virtual point pv located

at dv in the direction of fj max to define pn1 Finally, rn2 and its rn2 are determined under ALGORITHM-2

5.3 Unification function

In order to enable multiple swarms in close proximity to merge into a single swarm, ri adjusts Ti with respect to its local coordinate system and defines the position set of robots Du located within the range of du r computes ang Ti,pipu , where pipu is the vector starting from pi to a neighboring point puin Du, and defines a neighbor point pref that gives the minimum ang Ti,pipu between Ti and pipu If there exists pul, ri finds another neighbor point pum using the same method starting from pipul Unless pul exists, ri defines pref as prn Similarly, ri can decide a specific neighbor point pln while rotating 60 degrees counterclockwise from pipref The two points, denoted as prn and pln, are located at the farthest point in the right-hand or left-hand direction of pipu, respectively Next, a unification area A Ui is defined as the common area between A Ti in SB and the rest of the area in SB, where no element of Du exists Then, ri defines a set of robots in A Ui and selects the first neighbor rn1 In particular, the second neighbor position pn2 is defined such that the total distance from pn1 to pi can be minimized only through either prn or pln

(a) traveling direction Ti (b) unification area A Ui

Fig 9 Illustration of the unification function

5.4 Escape control

When ri detects an arena border within its SB as shown in Fig 10-(a), it checks whether i is equal to i Neighboring robots should always be kept du distance from ri Moreover, ri’s

current position pi and its next movement position pti remain unchanged for several time

steps, ri will find itself trapped in a dead-end passageway ri then attempts to find new

neighbors within the area A Ei to break the stalemate Similar to the unification function, ri adjusts Ti with respect to its local coordinate system and defines the position set of robots De located within SB As shown in Fig 10-(b), ri computes ang Ti,pipe , where pipu is the vector

starting from pi to a neighboring point pe in De, and defines a neighbor point rref that gives

the minimum ang Ti,pipe between Ti and pipu While rotating 60 degrees clockwise and

counterclockwise from pipref, respectively, ri can decide the specific neighbor points pln and

prn Employing pln and prn, the escape area A Ei is defined Then, ri adjusts a set of robots in

A Ei and selects the first neighbor rn1 In particular, the second neighbor position pn2 is determined under ALGORITHM-2

(a) encountered dead-end passageway (b) merging with another adjacent swarm Fig 10 Illustration of the escape function

6 Simulation results and discussion

This section describes simulation results that tested the validity of our proposed adaptive navigation scheme We consider that a swarm of robots attempts to navigate toward a stationary goal while exploring and adapting to unknown environmental conditions In such an application scenario, the goal is assumed to be either a light or odor source that can only be detected by a limited number of robots As mentioned in Section 3, the coordinated navigation is achieved without using any leader, identifiers, global coordinate system, and explicit communication We set the range of SB to 2.5 times longer than du

The first simulation demonstrates how a swarm of robots adaptively navigates in an environment populated with obstacles and dead-end passageway In Fig 11, the swarm navigates toward the goal located on the right hand side On the way to the goal, some of the robots detect a triangular obstacle that forces the swarm split into two groups from 7 sec (Fig 11-(c)) The rest of the robots that could not identify the obstacle just follow their

neighbors moving ahead After being split into two groups at 14 sec (Fig 11-(d)), each group maintains their local geometric configuration while navigating At 18 sec (Fig 11-(e)), some

robots happen to enter a dead-end passageway After they find themselves trapped, they attempt to escape from the passageway by just merging themselves into a neighboring

group from 22 sec to 32 sec (from Figs 11-(f)) to (k)) After 32 sec (Fig 11-(k)), simulation result shows that two groups merge again completely At 38 sec (Fig 11-(l)), the robots

successfully pass through the obstacles

Fig 11 Simulation results of adaptive flocking toward a stationary goal ((a)0 sec,(b)4 sec, (c)7 sec,(d)14 sec,(e)18 sec,(f)22 sec,(g)23 sec,(h)24 sec,(i)28 sec,(j)29 sec,(k)32 sec,(l)38sec)

Fig 12 shows the trajectories of individual robots in Fig 11 We could confirm that the

swarm was split into two groups due to the triangular obstacle located at coordinates (0,0)

If we take a close look at Figs 11-(f) through (j) (from 22 sec to 29 sec), the trapped ones

escaped from the dead-end passageway located at coordinates (x, 200) More important, after passing through the obstacles, all robots position themselves from each other at the desired interval du

Fig 12 Robot trajectory results for the simulation in Fig.11

Next, the proposed adaptive navigation is evaluated in a more complicated environmental condition as presented in Fig 13 On the way to the goal, some of the robots detect a rectangular obstacle that forces the swarm split into two groups in Fig 13-(b) After passing through the obstacle in Fig (d), the lower group encounters another obstacle in Fig 13-(e), and split again into two smaller groups in Fig 13-(g) Although several robots are trapped in a dead-end passageway, their local motions can enable them to escape from the dead-end passageway in Fig 13-(i) This self-escape capability is expected to be usefully exploited for autonomous search and exploration tasks in disaster areas where robots have

to remain connected to their ad hoc network Finally, for a comparison of the adaptive

navigation characteristics, three kinds of simulations are performed as shown in Figs 14

through 16 All the simulation conditions are kept the same such as du, the number of

robots, and initial distribution Fig 14 shows the behavior of mobile robot swarms without the partition and escape functions Here, a considerable number of robots are trapped in the dead-end passageway and other robots pass through an opening between the obstacle and the passageway by chance As compared with Fig 14, Fig 15 shows more robots pass through the obstacles using the partition function However, a certain number of robots remain trapped in the dead-end passageway because they have no self-escape function Fig

16 shows that all robots successfully pass through the obstacles using the proposed adaptive navigation scheme It is evident that the partition and escape functions will provide swarms

of robots with a simple yet efficient navigation method In particular, self-escape is one of the most essential capabilities to complete tasks in obstacle-cluttered environments that require a sufficient number of simple robots

Fig 13 Simulation results of adaptive flocking toward a stationary goal ((a)0 sec,(b)8 sec, (c)10 sec,(d)14 sec,(e)18 sec,(f)22 sec,(g)25 sec,(h)27 sec,(i)31 sec,(j)36)

Fig 14 Simulation results for flocking without partition and escape functions

Fig 15 Simulation results for flocking with only partition function

Fig 16 Simulation results for flocking with the partition and escape functions

7 Conclusions

This paper was devoted to developing a new and general coordinated adaptive navigation scheme for large-scale mobile robot swarms adapting to geographically constrained environments Our distributed solution approach was built on the following assumptions: anonymity, disagreement on common coordinate systems, no pre-selected leader, and no direct communication The proposed adaptive navigation was largely composed of four functions, commonly relying on dynamic neighbor selection and local interaction When each robot found itself what situation it was in, individual appropriate ranges for neighbor selection were defined within its limited sensing boundary and the robots properly selected their neighbors in the limited range Through local interactions with the neighbors, each robot could maintain a uniform distance to its neighbors, and adapt their direction of heading and geometric shape More specifically, under the proposed adaptive navigation, a group of robots could be trapped in a dead-end passage, but they merge with an adjacent group to emergently escape from the dead-end passage Furthermore, we verified the effectiveness of the proposed strategy using our in-house simulator The simulation results clearly demonstrated that the proposed algorithm is a simple yet robust approach to autonomous navigation of robot swarms in highly-cluttered environments Since our algorithm is local and completely scalable to any size, it

is easily implementable on a wide variety of resource-constrained mobile robots and platforms Our adaptive navigation control for mobile robot swarms is expected to be used in many applications ranging from examination and assessment of hazardous

environments to domestic applications

8 References

Balch, T & Hybinette, M (2000) Social potentials for scalable multi-robot formations, Proc

IEEE Int Conf Robotics and Automation, pp 73-80, IEEE

Correll, N., Bachrach, J., Vickery, D., & Rus, D (2009) Ad-hoc wireless network coverage

with networked robots that cannot localize, Proc IEEE Int Conf Robotics and

Automation, pp 3878 - 3885, IEEE

Esposito, J M & Dunbar, T W (2006) Maintaining wireless connectivity constraints for

swarms in the presence of obstacles, Proc IEEE Int Conf Robotics and Automation,

pp 946-951, IEEE

Folino, G & Spezzano, G (2002) An adaptive flocking algorithm for spatial clustering, In:

Parallel Problem Solving from Nature (LNCS), Yao, X., Burke, E., Lozano, J A., Smith,

J., Merelo-Guervos, J J., Bullinaria, J A., Rowe, J., Tino, P., Kaban, A., & Schwefel, H.-P (Ed.), Vol 2439, 924-933, Springer Berlin, ISBN: 978-3-540-23092-2

Fowler, T (2001) Mesh networks for broadband access, IEE Review, Vol 47, No 1, 17-22

Gu, D & Hu, H (2010) Distributed minmax filter for tracking and flocking, Proc IEEE/RSJ

Int Conf Intelligent Robots and Systems, pp 3562-3567, IEEE

Ikemoto, Y., Hasegawa, Y., Fukuda, T., & Matsuda, K (2005) Graduated spatial pattern

formation of robot group, Information Science, Vol 171, No 4, 431-445

Lam, M & Liu, Y (2006) ISOGIRD: an efficient algorithm for coverage enhancement in

mobile sensor networks, Proc IEEE/RSJ Int Conf Intelligent Robots and Systems, pp

1458-1463, IEEE

Lee, G & Chong, N Y (2009) A geometric approach to deploying robot swarms, Annals of

Mathematics and Artificial Intelligence, Vol 52, No 2 − 4, 257-280

Lee, G & Chong, N Y (2009-b) Decentralized formation control for small-scale robot teams

with anonymity, Mechatronics, Vol 19, No 1, 85-105

Lee, G & Chong, N Y (2008) Adaptive flocking of robot swarms: algorithms and

properties, IEICE Trans Communications, Vol E91 − B, No 9, 2848-2855

Lyengar, R., Kar, K., & Banerjee, S (2005) Low-coordination topologies for redundancy in

sensor networks, Proc 3rd Acm Int Sym Mobile Ad Hoc Networking and Computing,

pp 332-342, ACM

Nembrini, J., Winfield, A., & Melhuish, C (2002) Minimalist coherent swarming of wireless

networked autonomous mobile robots, Proc 7th Int Conf Simulation of Adaptive

Behavior, pp 373-382, IEEE

Olfati-Saber, R (2006) Flocking for mult-agnet dynamic systems: algorithms and theory,

IEEE Trans Automatic Control, Vol 51, No 3, 401-420

Ogren, P & Leonard, N E (2005) A convergent dynamic window approach to obstacle

avoidance, IEEE Trans Robotics and Automation, Vol 21, No 2, 188-195

Stocker, C W (1987) Flocks, herds, and schools: a distributed behavioral model, Computer

Graphics, Vol 21, No 4, 25-34

Sahin, E (2005) Swarm robotics: from sources of inspiration to domains of application, In:

Swarm Robotics (LNCS), Sahin, E & Spears, W M., (Ed.), Vol 3342, 10-20, Springer

Berlin, ISBN: 978-3-540-24296-3

Shucker, B., Murphey, T D., & Bennett, J K (2008) Convergence-preserving switching for

topology-dependent decentralized systems, IEEE Trans Robotics, Vol 24, No 6,

1405-1415

Slotine, J E & Li,W (1991) Applied nonlinear control, Prentice-Hall, ISBN: 0-13-040890-5 Spears, D., Kerr, W., & Spears, W M (2006) Physics-based robot swarms for coverage

problems, Int Jour.Intelligent Control and Systems, Vol 11, No 3, 124-140

Spears, W M., Spears, D., Hamann, J., & Heil, R (2004) Distributed, physics-based control

of swarms of vehicles, Autonomous Robots, Vol 17, No 2 − 3, 137-162

Stocker, S (1999) Models for tuna school formation, Mathematical Biosciences, Vol 156, No

1−2, 167-190

Wilson, E O (1976) Sociobiology: the new synthesis, Harvard University Press, ISBN:

0-674-00089-7

Yicka, J., Mukherjeea, B., & Ghosal, D (2008) Wireless sensor network survey, Computer

Networks, Vol 52, No 12, 2292-2330

Zarzhitsky, D., Spears, D., & Spears, W M (2005) Distributed robotics approach to chemical

plume tracing, Proc IEEE/RSJ Int Conf Intelligent Robots and Systems, pp 4034-4039,

IEEE